Lots of good ways to cook up a catfish, but you asked about frying.
Simplest is sometimes the best! Chill dressed catfish in some salt water, no longer than overnight. Shake off water and roll in cornmeal (can dust cornmeal with salt and pepper). Fry in oil or melted shortening in cast iron skillet, turning once. Best served hot, leftovers are OK warmed in oven for breakfast.
Fancy is good, too! Again, chill dressed catfish in some salt water, no longer than overnight. This works best if fish is chunks, steaks or fillets (not whole fish). Pat fish dry and dip in buttemilk, roll in mix of 1/2 flour, 1/2 cracker crumbs. Fry as above.